Methods and system for analysis and management of parametric yield

ABSTRACT

Impact on parametric performance of physical design choices for transistors is scored for on-current and off-current of the transistors. The impact of the design parameters are incorporated into parameters that measure predicted shift in mean on-current and mean off-current and parameters that measure predicted increase in deviations in the distribution of on-current and the off-current. Statistics may be taken at a cell level, a block level, or a chip level to optimize a chip design in a design phase, or to predict changes in parametric yield during manufacturing or after a depressed parametric yield is observed. Further, parametric yield and current level may be predicted region by region and compared with observed thermal emission to pinpoint any anomaly region in a chip to facilitate detection and correction in any mistakes in chip design.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. patent application Ser. No.13/216,362, filed on Aug. 24, 2011, which is a divisional of U.S. patentapplication Ser. No. 11/876,853, filed Oct. 23, 2007, now U.S. Pat. No.8,042,070 issued on Oct. 18, 2011 the entire content and disclosures ofwhich are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to methods and systems for analyzing andimproving parametric yield in semiconductor device manufacturing.

BACKGROUND OF THE INVENTION

With continual scaling of dimensions in semiconductor devices andincrease in the number of gates per chip, yield management insemiconductor manufacturing has become critical for economical andprofitable operation of chip manufacturing facilities. Referring to FIG.1, past trends up to 65 nm technology node and forecast for futuretechnology nodes show three components of yield loss including randomdefect yield loss, process limited yield loss, and parametric yieldloss.

Random defect yield loss is the yield loss due to random defectsgenerated during manufacturing of a semiconductor chip. As feature sizesshrink in a semiconductor chip, functionality of the semiconductor chipis more readily disturbed by random defects generated duringsemiconductor processing steps, resulting in increased in the randomdefect yield loss in successive technology generation. While the impactof random defects on yield becomes more severe in successive technologygenerations, semiconductor chip manufacturing facility automation andprocess enhancements tend to reduce generation of random defects andmitigate the increase in the random defect yield loss.

Process limited yield loss is the yield loss due to failure to controlprocess parameters within specification. Process limited yield loss isthus due to an out-of-specification process parameter such as athickness of a film, recess depth of a structure in a semiconductorsubstrate, and composition of a material. Inherent variability insemiconductor manufacturing processes causes some semiconductor chips tobe out-of-specification for at least one process parameter. If the outof spec condition results in a short or open due then the chip is saidto suffer from Process limited yield. Note, not all out of spec processparameters result in process limited yield. Increase in complexity ofprocessing steps contributes to increase in the process limited yieldloss, while improvement in process control tends to mitigate the impactof the processing steps on the process limited yield.

Parametric yield loss is the yield loss due to the fraction ofmanufactured semiconductor chips that do not meet performancespecifications among the chips that do not suffer from random defectyield loss or process limited yield loss. In other words, the chipsaffected by the parametric yield loss do not have random defects orout-of-specification process parameters that result in a hard failure,such as a short or an open. If an out of spec process parameter does notresult in a hard failure, such as a short or an open, but doescontribute to a deviation from modeled simulated behavior, and thisdeviation contributes to the chip not meeting the performancespecification, then the chip is said to suffer from parametric orcircuit limited yield. Additionally, at least one of designspecification for the chip, which may be, for example, circuit timing orpower consumption in on-state or in off-state, is out of specification.The cause of the failure of the chip to meet the design specificationmay not be attributed to the random defect yield loss or process limitedyield loss, but is attributed to statistical distribution of performanceof individual semiconductor devices in the semiconductor chip. Thefraction of the number of chips that do not meet the devicespecification due to these reasons relative to the number of chips thatare not affected by random defect yield loss or process limited yieldloss is the parametric yield loss, which is sometimes also referred toas “circuit limited yield loss.” Thus parametric yield loss has both arandom, statistical component and a systematic component.

The impact of parametric yield loss increases in each succeedingtechnology node since more devices are integrated into a semiconductorchip. Recognizing the severe impact of the parametric yield loss,“design for manufacturability” (DFM) has been promoted as a concept. Inessence, designers factor in potential yield impact of a particulardesign. While being a useful concept, design for manufacturability doesnot provide algorithms or methodology for systematically increasingparametric yield. Instead, it is a general recommendation to avoiddesigning circuits that may potentially cause performance problems.

It should be recognized, however, that employing an aggressive designthat may potentially cause parametric yield issues is necessary todesign a high performance chip. The difficult part is to estimate thebalance between a potential gain in performance of an aggressive designand increase in parametric yield, i.e., decrease in parametric yieldloss, of a conservative design.

Referring to FIG. 2, an exemplary prior art method for designing asemiconductor chip is shown in a flow chart 200. Referring to step 210,functional requirements of a chip are defined. The chip may be aprocessor, a volatile or non-volatile memory chip, or a system-on-chip(SoC) having multiple embedded components. Functional requirementsinclude the nature of the chip as well as performance goals of the chip.

Referring to step 220, an electronic system level (ESL) description isgenerated based on the functional requirements of the chip. Electronicsystem level description and verification is a design methodology thatfocuses on the higher abstraction level without regard to lower levelimplementation. The goal of the ESL description is to enhance theprobability of a successful implementation of functionality. Appropriateabstractions are utilized to generate a global level understanding ofthe chip to be designed. To this end, a high level programming languagesuch as C or C++ is employed as an abstract modeling language to modelthe behavior of the entire system to be contained in a chip. Typically,this process is manual, although automation of this step by electronicdesign automaton (EDA) has been under investigation.

Referring to step 230, a register transfer level (RTL) description isgenerated from the electronic system level (ESL) description in the nextchip design phase. Register transfer level (RTL) description is adescription of a semiconductor chip design in terms of its operation.Specifically, the behavior of a circuit is defined in terms of datatransfer, or flow of signals between hardware registers in the RTLdescription. Logical operations are performed on the data. A hardwaredescription language (HDL) such as Verilog™ or VHDL™ is employed tocreate high-level representations of a circuit, from which lower levelrepresentations and ultimately actual discrete devices and wiring may bederived.

Referring to step 240, logic synthesis is performed to convert the RTLdescription in the form of the hardware description language (HDL) intoa gate level description of the chip by a logic synthesis tool.Specifically, the gate level description is a discrete netlist of logicgate primitives, or “Boolean logic primitives.”

Referring to step 250, placement and routing tools utilize the resultsof the logic synthesis to create a physical layout for the chip. Logicgates and other device components of the netlist are placed in a“layout,” or a chip design. The chip design is then routed, i.e., wiresare added to the placed components to provide interconnection betweenthe components' signal and power terminals. Typically, this process isperformed with tools employing electronic design automation (EDA)features.

Referring to step 260, power analysis and timing analysis is performed.It is noted that the exemplary prior art method scales power generationby scaling of a nominal device or multiple nominal devices. In otherwords, only the device type and device size are employed in the poweranalysis. The power analysis and the timing analysis are performed tocheck the chip design for functionality.

Referring to step 270, the chip design is analyzed to extract designspecification. For example, timing analysis may be employed at thispoint to specify timing delay and expected chip operating frequency.Further, nominal leakage currents are estimated to specify powerconsumption of the chip.

Referring to FIG. 3, an exemplary prior art semiconductor chipmanufacturing sequence including the steps of chip design is shown in aflow chart 300. Referring to step 310, a semiconductor chip design isprovided as described in steps 210-260 of the flow chart 200 in FIG. 2.Referring to step 312, design specification is generated for the chip asin step 270 of the flow chart 200 in FIG. 2.

Referring to step 320, data preparation is performed on the chip designto generate various mask levels, which may then be transmitted to a“mask house,” or a mask fabrication facility to initiate fabrication ofphysical masks to be employed in manufacturing of semiconductor chips.Various “design comps,” or compensations to instances in design levelsmay be performed as part of data preparation. The mask housemanufactures physical masks that may be subsequently employed inlithographic tools according to the mask level designs.

Referring to step 330, semiconductor chips are manufactured in asemiconductor chip fabrication facility. Typically, the semiconductorchips are manufactured on a semiconductor substrate such as a siliconsubstrate. Various semiconductor processing steps including lithography,deposition, and etching are employed.

Referring to step 340, the manufactured semiconductor chips are testedand characterized for functionality. Dysfunctional chips are sorted out.Operating frequency, on-state leakage, and off-state leakage aremeasured on functional chips.

Referring to step 350, parametric yield, i.e., circuit limited yield(CLY), is calculated for the group of semiconductor chips that do notsuffer from random defect yield loss or process limited yield loss.Assuming a normal scenario in which the random defect yield loss and theprocess limited yield loss of the manufacturing process are withinexpected ranges, delivery of sufficient number of chips to a customerdepends on the parametric yield loss. If the parametric yield exceeds aminimum parametric yield target value, sufficient number of chipsmeeting the design specification may be shipped to a customer, as shownin the step 360. If the parametric yield is below a minimum targetvalue, not enough chips meeting the design specification are availablefor shipping, as shown in step 379.

In this case, few courses of systematic action are available to thesemiconductor chip manufacturing facility for investigation of thesource of the depressed parametric yield. While some methods are knownin the art for diagnosing depressed process limited yield such assorting the semiconductor chips by processing history or processvariations, depressed parametric yield is much more difficult toinvestigate since the depressed parametric yield is correlated tospecific design features of the semiconductor chip.

In financial perspective, when a semiconductor chip manufacturingfacility commits to manufacture semiconductor chips based on an unknownchip design, the level of parametric yield loss is unpredictable fromthe perspective of the semiconductor chip manufacturing facility, whilea customer generating a new chip design may have a vague idea of thelevel of expected parametric yield. Neither party has a goodunderstanding on what level of parametric yield should be expected onthe new chip design. Thus, lack of precise estimation of the parametricyield on the new chip design exposes a semiconductor chip manufacturingfacility to a financial uncertainty, while the customer submitting thenew design is not provided with any guidance on how to improve thedesign to enhance the parametric yield.

In view of the above, there exists a need for a system and methods foranalyzing and managing parametric yield on a semiconductor chip during achip design phase.

Further, there exists a need for a system and methods for analyzing andmanaging parametric yield on a semiconductor chip during a chipmanufacturing phase or after a depressed parametric yield is observed intesting.

Yet further, there exists a need for a system and methods for predictingparametric yield at various levels to compare with observed data so thatany anomaly in design may be found during testing of manufacturedsemiconductor chips.

SUMMARY OF THE INVENTION

The present invention addresses the needs described above by providing asystem and methods for analyzing and managing parametric yield on asemiconductor chip during a chip design phase, a chip manufacturingphase, and after a depressed parametric yield is observed as well as asystem and methods for comparing observed parametric yield with aparametric yield model.

In the present invention, impact on parametric performance of physicaldesign choices for transistors is scored for on-current and off-currentof the transistors. Design parameters affecting the on-current andoff-current of the transistors include dimensions of various features ofthe transistor relative to nearby structures as well asacross-chip-length-variation (ACLV) and corner rounding stress effects.The impact of the design parameters are incorporated into parametersthat measure predicted shift in mean on-current and mean off-current andparameters that measure predicted increase in deviations in thedistribution of the on-current and the off-current. Statistics may betaken at a cell level, a block level, or a chip level to optimize a chipdesign in a design phase, or to predict changes in parametric yieldduring manufacturing or after a depressed parametric yield is observed.Further, parametric yield and current level may be predicted region byregion and compared with observed thermal emission to pinpoint anyanomaly region in a chip to facilitate detection and correction in anymistakes in chip design.

According to an aspect of present invention, a system for designing asemiconductor chip is provided, which comprises:

threshold voltage adder calculation means for calculating a calculatedthreshold voltage adder for a device within a subset of a semiconductorchip design including an effect of at least one design parameter of thesubset other than inherent geometric dimensions and inherentcharacteristics of the device; and

parametric yield estimation means for estimating a parametric yieldestimation value of the subset of the semiconductor chip design, whereinthe parametric yield estimation value is based on the calculatedthreshold voltage adder.

In one embodiment, the system further comprises at least one of:

average on-current adder calculation means for calculating an averageon-current adder for the subset of the semiconductor chip design; and

average off-current adder calculation means calculating an averageoff-current adder for the subset of the semiconductor chip design,

wherein the average on-current adder is an average deviation ofon-current of the subset from a scaling-estimated on-current, which isobtained by scaling of at least one nominal device, due to the designparameters of the subset other than inherent geometric dimensions andinherent characteristics of at least one device of the subset, andwherein the average off-current adder is an average deviation ofoff-current of the subset from a scaling-estimated off-current, which isobtained by scaling of at least one nominal device, due to the designparameters of the subset other than inherent geometric dimensions andinherent characteristics of at least one device of the subset, andwherein the parametric yield estimation value is based on at least oneof the average on-current adder and the average off-current adder.

In another embodiment, the subset comprises a cell containing onefunctional semiconductor device unit within the semiconductor chipdesign a plurality of semiconductor device units within thesemiconductor chip design.

In even another embodiment, the design parameters of the subsetcomprises at least one of positional relationship between an element ofthe subset and another element of the subset and positional relationshipbetween an element of the subset and another element of another subsetin the semiconductor chip design.

In yet another embodiment, the system further comprises:

logic synthesis means for performing logic synthesis to generate anetlist of the semiconductor chip design, wherein the semiconductordesign is the netlist; and

flow control means for controlling flow of a sequence of operating thesystem, wherein the flow control means directs the flow to a step inwhich the netlist is modified if the parametric yield estimation valuedoes not exceeds a target value.

In still another embodiment, the system further comprises:

placement and routing means for placing and routing a netlist of thesemiconductor chip design to generate a chip layout, wherein thesemiconductor design is the chip layout; and

flow control means for controlling flow of a sequence of operating thesystem, wherein the flow control means directs the flow to a step inwhich the chip layout is modified if the parametric yield estimationvalue does not exceeds a target value.

In still yet another embodiment, the system further comprises at leastone of:

incremental on-current deviation calculation means for calculating anincremental on-current deviation for the subset of the semiconductorchip design, wherein the incremental on-current deviation is anincrement in statistical deviation of on-current of the subset of thesemiconductor chip deign from a scaling-estimated statistical deviationof on-current, which is obtained by scaling of statistical deviation ofon-current of at least one nominal device, due to the design parametersof the subset other than inherent geometric dimensions and inherentcharacteristics of at least one device of the subset; and

incremental off-current deviation calculation means for calculating anincremental off-current deviation for the subset of the semiconductorchip design, wherein the incremental off-current deviation is anincrement in statistical deviation of off-current of the subset of thesemiconductor chip deign from a scaling-estimated statistical deviationof off-current, which is obtained by scaling of statistical deviation ofoff-current of at least one nominal device, due to the design parametersof the subset other than inherent geometric dimensions and inherentcharacteristics of devices in the subset.

In a further embodiment, the system further comprises at least one of:

on-current distribution calculation means for calculating statisticaldistribution of on-current within the subset; and

off-current distribution calculation means for calculating statisticaldistribution of off-current within the subset.

In an even further embodiment, the system further comprises at least oneof:

on-state temperature distribution calculation means for calculatingon-state temperature distribution of a semiconductor chip manufacturedwith the semiconductor design; and

off-state temperature distribution calculation means for calculatingoff-state temperature distribution of the semiconductor chipmanufactured with the semiconductor design.

In a yet further embodiment, the on-state temperature distribution iscalculated based on the statistical distribution of the on-currentwithin the subset, and wherein the off-state temperature distribution iscalculated based on the statistical distribution of the off-currentwithin the subset.

In another aspect of the present invention, a system for analyzingparametric yield of a semiconductor chip design is provided, whichcomprises:

threshold voltage adder calculation means for calculating a calculatedthreshold voltage adder for a device within a subset of a semiconductorchip design including an effect of at least one design parameter of thesubset other than inherent geometric dimensions and inherentcharacteristics of the device;

parametric yield estimation means for estimating a parametric yieldestimation value of the subset of the semiconductor chip design, whereinthe parametric yield estimation value is based on the calculatedthreshold voltage adder;

a tester for generating at least one measured parametric yield value bytesting at least one semiconductor chip that is manufactured accordingto the semiconductor chip design; and

parametric yield comparison means for comparing the parametric yieldestimation value and the at least one measured parametric yield value.

In one embodiment, the design parameters of the subset comprises atleast one of positional relationship of an element of the subset toanother element of the subset and positional relationship of an elementof the subset to another subset in the semiconductor chip design.

In another embodiment, the system further comprises at least one of:

incremental on-current deviation calculation means for calculating anincremental on-current deviation for the subset of the semiconductorchip design, wherein the incremental on-current deviation is anincrement in statistical deviation of on-current of the subset of thesemiconductor chip deign from a scaling-estimated statistical deviationof on-current, which is obtained by scaling of statistical deviation ofon-current of at least one nominal device, due to the design parametersof the subset other than inherent geometric dimensions and inherentcharacteristics of at least one device of the subset; and

incremental off-current deviation calculation means for calculating anincremental off-current deviation for the subset of the semiconductorchip design, wherein the incremental off-current deviation is anincrement in statistical deviation of off-current of the subset of thesemiconductor chip deign from a scaling-estimated statistical deviationof off-current, which is obtained by scaling of statistical deviation ofoff-current of at least one nominal device, due to the design parametersof the subset other than inherent geometric dimensions and inherentcharacteristics of devices in the subset.

In even another embodiment, the system comprises at least one of:

on-current distribution calculation means for calculating statisticaldistribution of on-current within the subset; and

off-current distribution calculation means for calculating statisticaldistribution of off-current within the subset.

In yet another embodiment, the system further comprises:

a measured process parameter database that stores measured processparameter values that are measured during manufacturing of the at leastone semiconductor chip;

a process model for correlating variations in the measured processparameter values with the at least one measured parametric yield value;and

process model fitting means for fitting discrepancy between theparametric yield estimation value and the at least one measuredparametric yield value with the measured process parameter values toimprove accuracy of the process model.

In still another embodiment, the system further comprises parametricestimation value change simulation means for simulating a change in theparametric estimation value in response to changes in the designparameter.

According to yet another aspect of the present invention, a system foridentifying a location of anomalous functionality on a semiconductorchip is provided, which comprises:

at least one of on-current distribution calculation means forcalculating spatial distribution of on-current within the semiconductorchip and off-current distribution calculation means for calculatingspatial distribution of off-current within the semiconductor chip;

current-to-temperature conversion means for converting one of thespatial distribution of on-current and the spatial distribution of theoff-current into an estimated spatial temperature distribution map; and

temperature distribution measurement means for generating a measuredtemperature distribution map of the semiconductor chip in an on-state oran off-state.

In one embodiment, the system comprises threshold voltage addercalculation means for calculating a calculated threshold voltage adderfor a device within a subset of a semiconductor chip design including aneffect of at least one design parameter of the subset other thaninherent geometric dimensions and inherent characteristics of thedevice, wherein at least one of the spatial distribution of on-currentand the spatial distribution of off-current is based on the calculatedthreshold voltage adder.

In another embodiment, the system further comprises:

a measured process parameter database that stores measured processparameter values that are measured during manufacturing of thesemiconductor chip;

a process model for correlating the measured process parameter valueswith the measured temperature distribution map; and

process model fitting means for fitting discrepancy between the measuredtemperature distribution map and at least one of the spatialdistribution of on-current and the spatial distribution of off-currentto improve accuracy of the process model.

In yet another embodiment, the system further comprises temperaturedistribution comparison means for comparing the estimated spatialtemperature distribution map with the measured temperature distributionmap of the semiconductor chip.

According to even another aspect of the present invention, a method ofdesigning a semiconductor chip is provided, which comprises:

calculating a calculated threshold voltage adder for a device within asubset of a semiconductor chip design including an effect of at leastone design parameter of the subset other than inherent geometricdimensions and inherent characteristics of the device; and

estimating a parametric yield estimation value of the subset of thesemiconductor chip design, wherein the parametric yield estimation valueis based on the calculated threshold voltage adder.

In one embodiment, the method comprises at least one of:

calculating an average on-current adder for the subset of thesemiconductor chip design; and

calculating an average off-current adder for the subset of thesemiconductor chip design,

wherein the average on-current adder is an average deviation ofon-current of the subset from a scaling-estimated on-current, which isobtained by scaling of at least one nominal device, due to the designparameters of the subset other than inherent geometric dimensions andinherent characteristics of at least one device of the subset, andwherein the average off-current adder is an average deviation ofoff-current of the subset from a scaling-estimated off-current, which isobtained by scaling of at least one nominal device, due to the designparameters of the subset other than inherent geometric dimensions andinherent characteristics of at least one device of the subset, andwherein the parametric yield estimation value is based on at least oneof the average on-current adder and the average off-current adder.

In another embodiment, the method further comprises:

performing logic synthesis to generate a netlist of the semiconductorchip design, wherein the semiconductor design is the netlist; and

controlling flow of a sequence of operating the system, wherein the flowcontrol means directs the flow to a step in which the netlist ismodified if the parametric yield estimation value does not exceeds atarget value.

In even another embodiment, the method further comprises:

placing and routing a netlist of the semiconductor chip design togenerate a chip layout, wherein the semiconductor design is the chiplayout; and

controlling flow of a sequence of operating the system, wherein the flowcontrol means directs the flow to a step in which the chip layout ismodified if the parametric yield estimation value does not exceeds atarget value.

In yet another embodiment, the method further comprises at least one of:

calculating an incremental on-current deviation for the subset of thesemiconductor chip design, wherein the incremental on-current deviationis an increment in statistical deviation of on-current of the subset ofthe semiconductor chip deign from a scaling-estimated statisticaldeviation of on-current, which is obtained by scaling of statisticaldeviation of on-current of at least one nominal device, due to thedesign parameters of the subset other than inherent geometric dimensionsand inherent characteristics of at least one device of the subset; and

calculating an incremental off-current deviation for the subset of thesemiconductor chip design, wherein the incremental off-current deviationis an increment in statistical deviation of off-current of the subset ofthe semiconductor chip deign from a scaling-estimated statisticaldeviation of off-current, which is obtained by scaling of statisticaldeviation of off-current of at least one nominal device, due to thedesign parameters of the subset other than inherent geometric dimensionsand inherent characteristics of devices in the subset.

In still another embodiment, the method further comprises at least oneof:

calculating statistical distribution of on-current within the subset;and

calculating statistical distribution of off-current within the subset.

In still yet another embodiment, the method further comprises at leastone of:

calculating on-state temperature distribution of a semiconductor chipmanufactured with the semiconductor design; and

calculating off-state temperature distribution of the semiconductor chipmanufactured with the semiconductor design.

According to still another aspect of the present invention, a method ofanalyzing parametric yield of a semiconductor chip design is provided,which comprises:

calculating a calculated threshold voltage adder for a device within asubset of a semiconductor chip design including an effect of at leastone design parameter of the subset other than inherent geometricdimensions and inherent characteristics of the device;

estimating a parametric yield estimation value of the subset of thesemiconductor chip design, wherein the parametric yield estimation valueis based on the calculated threshold voltage adder;

generating at least one measured parametric yield value by testing atleast one semiconductor chip that is manufactured according to thesemiconductor chip design; and

comparing the parametric yield estimation value and the at least onemeasured parametric yield value.

In one embodiment, the method further comprises at least one of:

calculating an incremental on-current deviation for the subset of thesemiconductor chip design, wherein the incremental on-current deviationis an increment in statistical deviation of on-current of the subset ofthe semiconductor chip deign from a scaling-estimated statisticaldeviation of on-current, which is obtained by scaling of statisticaldeviation of on-current of at least one nominal device, due to thedesign parameters of the subset other than inherent geometric dimensionsand inherent characteristics of at least one device of the subset; and

calculating an incremental off-current deviation for the subset of thesemiconductor chip design, wherein the incremental off-current deviationis an increment in statistical deviation of off-current of the subset ofthe semiconductor chip deign from a scaling-estimated statisticaldeviation of off-current, which is obtained by scaling of statisticaldeviation of off-current of at least one nominal device, due to thedesign parameters of the subset other than inherent geometric dimensionsand inherent characteristics of devices in the subset.

In another embodiment, the method further comprises at least one of:

calculating statistical distribution of on-current within the subset;and

calculating statistical distribution of off-current within the subset.

In even another embodiment, the method further comprises:

storing measured process parameter values that are measured duringmanufacturing of the at least one semiconductor chip;

correlating variations in the measured process parameter values with theat least one measured parametric yield value with a process model; and

fitting discrepancy between the parametric yield estimation value andthe at least one measured parametric yield value with the measuredprocess parameter values to improve accuracy of the process model.

In yet another embodiment, the method further comprises simulating achange in the parametric estimation value in response to changes in thedesign parameter.

According to still yet another aspect of the present invention, a methodof identifying a location of anomalous functionality on a semiconductorchip is provided, which comprises:

calculating at least one of spatial distribution of on-current withinthe semiconductor chip and spatial distribution of off-current withinthe semiconductor chip;

converting one of the spatial distribution of on-current and the spatialdistribution of the off-current into an estimated spatial temperaturedistribution map; and

generating a measured temperature distribution map of the semiconductorchip in an on-state or an off-state.

In one embodiment, the method further comprises calculating a calculatedthreshold voltage adder for a device within a subset of a semiconductorchip design including an effect of at least one design parameter of thesubset other than inherent geometric dimensions and inherentcharacteristics of the device, wherein at least one of the spatialdistribution of on-current and the spatial distribution of off-currentis based on the calculated threshold voltage adder.

In another embodiment, the method further comprises:

storing measured process parameter values that are measured duringmanufacturing of the semiconductor chip;

correlating the measured process parameter values with the measuredtemperature distribution with a process model; and

fitting discrepancy between the measured temperature distribution mapand at least one of the spatial distribution of on-current and thespatial distribution of off-current to improve accuracy of the processmodel.

In yet another embodiment, the method further comprises comparing theestimated spatial temperature distribution map with the measuredtemperature distribution map of the semiconductor chip, wherein alocation of discrepancy is identified as the location of anomalousfunctionality.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a graph showing trends of various yield loss components atsuccessive semiconductor technology nodes.

FIG. 2 is a flow chart for a prior art method for generating asemiconductor chip design.

FIG. 3 is a flow chart for a prior art method for manufacturingsemiconductor chips based on a semiconductor chip design.

FIG. 4 is a graph showing an exemplary method calculating a thresholdvoltage (Vt) adder based on proximity of a transistor to an adjacentwell as well as a width of the transistor according to the presentinvention.

FIG. 5 is a flow chart for operating an exemplary system for designing asemiconductor device that incorporates parametric yield analysisaccording to the present invention.

FIG. 6 is a flow chart for operating an exemplary system for analyzingparametric yield of a semiconductor design according to the presentinvention.

FIG. 7 is a flow chart for operating an exemplary system for identifyinga location of anomalous functionality on a semiconductor chip accordingto the present invention.

FIG. 8 is an estimated spatial temperature distribution map for asemiconductor chip derived from a corresponding semiconductor chipdesign according to the present invention.

FIG. 9 is a measured temperature distribution map measured on asemiconductor chip.

DETAILED DESCRIPTION OF THE INVENTION

As stated above, the present invention relates to methods and systemsfor analyzing and improving parametric yield in semiconductor devicemanufacturing, which are now described in detail with accompanyingfigures. It is noted that like and corresponding elements mentionedherein and illustrated in the drawings are referred to by like referencenumerals.

In a transistor, the distance between source and drain regions of thetransistor and an edge of a well containing the source and drain regionsaffects the threshold voltage of the transistor. Such effects are knownin the art as well proximity effects. U.S. Pat. No. 7,089,513 to Bard etal. describes well proximity effects and is herein incorporated byreference.

Due to well proximity effects, threshold voltages of the p-type fieldeffect transistors of the same category that differ only by the size,i.e., the width of the gate that is the dimension of an active areaabutting a gate dielectric along the direction perpendicular to thedirection of current flow, are affected not only by the size of thep-type field effect transistors but also by the proximity of the edge ofthe active area to a nearby n-type well.

In general, the threshold voltage of a transistor depends not only oninherent geometric dimensions and inherent characteristics andcomposition of components of the transistor but also on designparameters of a subset of a semiconductor chip including the transistor.The design parameters contain at least one element that is external tothe transistor. As an example, the well proximity effect involves designparameters of a subset of a semiconductor chip, in which the subsetincludes the transistor and the well containing the transistor. Thelocation of the edge of the well is not a component of the transistor.Therefore, the edge of the well is external to the transistor. However,a design parameter, which in this case is the distance between thesource and drain regions and the edge of the well, affects the thresholdvoltage of the transistor. Therefore, a design parameter that of thesubset of the semiconductor chip other than inherent geometricdimensions and inherent characteristics of the transistor affectscharacteristics of the transistor, and specifically, affects thethreshold voltage of the transistor.

Referring to FIGS. 4, a graph showing variations in threshold voltage(Vt) adder values for p-type field effect transistors due to proximityto an n-well edge as well as the size of the p-type field effecttransistors. The threshold voltage (Vt) adder is an average deviation ofthe threshold voltage of a transistor from a nominal transistor. Anominal transistor is an idealized transistor representing a class oftransistors having a similar feature. For example, a nominal transistormay have a fixed gate length and a fixed gate width and may be embeddedin a semiconductor chip in a specified environment. The specifiedenvironment may be a nested environment, which is an environment inwhich a plurality of nominal transistor are arranged in aone-dimensional or a two-dimensional array, or may be an isolatedenvironment, which is an environment in which the nominal device isisolated by surrounding electrical isolation structures.

Due to statistical nature of semiconductor processing steps, andespecially due to stochastic nature of ion implantation processingsteps, the threshold voltage of a nominal transistor has a statisticaldistribution. A nominal threshold voltage of a nominal device refers toa statistical average of a threshold voltage distribution measured on anensemble of nominal devices. Threshold voltage distribution inherentlyhas a non-zero deviation for the threshold voltage for the nominaldevices. In case the threshold voltage distribution has a form of aGaussian distribution, a standard deviation may be defined. Since actualthreshold voltage distributions are typically Gaussian, presence of astandard deviation in the threshold voltage distributions is hereinassumed.

Of the two variables used in this graph, the first variable is a gatewidth, which is the width of the overlap of the gate of the transistorwith the active area of the transistor that is measured in the directionperpendicular to the current flow between the source and the drain. Thegate width is a variable derived from inherent geometric dimensions andinherent characteristics of the p-type field effect transistors. Thesecond variable is well edge proximity, which is the distance betweenthe source and drain regions of the p-type transistor to a nearest edgeof the n-well that contains the p-type filed effect transistor is avariable that is external to the p-type field effect transistors. Thus,the well edge proximity may not be derived from inherent geometricdimensions and inherent characteristics of a p-type field effecttransistor alone. Extraction of the second parameter requires data froma subset of a semiconductor chip design such that the subset contains acomponent, which in this case is an n-well, other than the p-type fieldeffect transistor. Thus, access to, and consideration of, designparameters of a subset of a semiconductor chip design enablescalculation of expected shift in transistor characteristics includingany deviation in the threshold voltage due to the design parametersinternal and external to the transistor.

For a given width of the gate and a given value for well edge proximity,a distribution of values is observed in measured threshold voltage of atransistor. The difference between measured threshold voltage of atransistor having inherent geometric dimensions and inherentcharacteristics and design parameters of a subset of a semiconductorchip design external to the transistor and the nominal threshold voltageof a nominal transistor is the threshold voltage (Vt) adder. The designparameters that may not be directly obtained from the design of thetransistor alone are herein referred to as external design parameters ofthe transistor. The design parameters that may be obtained from thedesign of the transistor alone are herein referred to as inherent designparameters of the transistor. Due to the statistical nature of theeffect of the inherent and external design parameters and thresholdvoltage distribution of nominal devices, the threshold voltage adder hasa distribution of for each set of design parameters. Statisticalquantities may be defined for the threshold voltage adder for each setof design parameters.

In the case of FIG. 4, solid curves represent a fit for nominalthreshold voltage adder values for the p-type field effect transistorfor the specified design parameters, i.e., the gate width and the welledge proximity. Nominal threshold voltage adder is an average shift inthe threshold voltage from the nominal threshold voltage due to theinherent and external design parameters. The nominal threshold voltageadder may be positive or negative. Other statistical quantities such asdeviation of threshold voltage adder and various percentile values,e.g., 1 percentile values, 5 percentile values, 95 percentile values, 99percentile values, as well as maximum and minimum observed values for agiven number of samples may be measured and mathematically fitted. Thedeviation of threshold voltage adder is the deviation of thedistribution of the threshold voltage adder, which is the distributionof the shift in the threshold voltage from the nominal thresholdvoltage.

In general, the effect of inherent design parameters and external designparameters is modeled by building a macro, or a test structure, thatmeasures the effect of the inherent design parameters and externaldesign parameters on manufactured semiconductor test chips. Methods ofmeasuring the effect of inherent design parameters such as gate lengthand gate width are known in the art. According to the present invention,the effect of external design parameters are also measured andincorporated into a compact model, which is a model for predictingperformance of a semiconductor device such as a transistor.

The external design parameters may include positional relationship of anelement of a subset of a semiconductor chip design that contains adevice to be characterized and another element of the subset of thesemiconductor chip design. One of the two elements may, or may not, be acomponent of the device. For example, the device may be a transistor,the subset may comprise the transistor and a well in which thetransistor is placed, the element may be source and drain regions, andthe other element may be an edge of the well. In this case, one of thetwo elements is a component of the transistor.

Alternately, the external design parameters may include positionalrelationship of an element of a subset of a semiconductor chip designthat does not contain a device to be characterized and another elementof the subset of the semiconductor chip design that does not contain thedevice. For example, the device may be a transistor, the subset maycomprise the device and two stress-generating structure located adjacentto the device, and each of the two elements may be one of the twostress-generating structures. In this case, none of the two elementscomprises a component of the transistor.

Yet alternately, the external design parameters may include positionalrelationship of a first element of a first subset of a semiconductorchip design that contains a device to be characterized and a secondelement of a second subset of the semiconductor chip design. The firstelement may, or may not, be a component of the device. For example, thedevice may be a transistor, the first subset may comprise the transistorand a first well in which the transistor is placed, the first elementmay be source and drain regions, the second subset may comprise anotherwell located adjacent to the first well, and the second element may bean edge of the second well. In this case, the first element is acomponent of the device. In another example, the device may be atransistor, the first subset may comprise the transistor and a firstwell in which the transistor is placed, the first element may be an edgeof the first well, the second subset may comprise another well locatedadjacent to the first well, and the second element may be an edge of thesecond well. In this case, the first element is not a component of thedevice.

Non-limiting examples of external design parameters that may be employedto evaluate the effect on the threshold voltage adder include distanceand orientation of well edges relative to an element of a transistor,distance and orientation of edges of stress-generating structures suchas embedded stress-generating materials or stress-generating dielectricliners relative to an element of the transistor, and distance andorientation of elements of other semiconductor devices relative to thetransistor and among themselves. Further, power density during anon-state or an off-state of the semiconductor chip within the subset ofthe semiconductor chip design may be employed to estimate thetemperature of the portion of the semiconductor chip design to assessthe impact of ambient temperature on the threshold voltage adder.

The effect of the inherent design parameters and external designparameters is then incorporated into threshold voltage adder calculationmeans such as a compact model. The compact model according to thepresent invention has the capability to calculate nominal thresholdvoltage adder and other statistical quantities such as deviation ofthreshold voltage adder in addition to other device characteristicsprediction capabilities known in the art. The threshold voltage addercalculation means may alternately be a program dedicated to calculationof the threshold voltage adder values. The threshold voltage adder thuscalculated is herein referred to as “calculated threshold voltage adder”to be differentiated from measured values of threshold voltage adder. Itis noted that the calculated threshold voltage adder is not necessarilya scalar value for a functional semiconductor device, but preferably andgenerally, a distribution having an average value and associatedstatistical quantities such as deviations and quantiles.

A “mean calculated threshold voltage adder” is a mean of the calculatedthreshold voltage adder, which is a distribution. A “deviation ofcalculated threshold voltage adder” is a standard deviation of thecalculated threshold voltage adder. Mathematically,

$\begin{matrix}{{{\Delta \; {Vt}^{mean}} = {\sum\limits_{i = 1}^{n}\; {\Delta \; {Vt}_{i}^{mean}}}},{and}} & \left( {{Equation}\mspace{14mu} 1} \right) \\{{{\sigma_{Vt}^{2} - \sigma_{{Vt}\; \_ \; 0}^{2}} = {\sum\limits_{i = 1}^{n}\; {\Delta \left( \sigma_{{Vt}\; \_ \; i}^{2} \right)}}},} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

wherein ΔVt^(mean) is the mean calculated threshold voltage adder of adevice, i.e., the transistor on which the calculated threshold voltageadder as a distribution is calculated, n is the total number of thedesign parameters that are related to the threshold voltage adder of thetransistor, and ΔVt_(i) ^(mean) is a contribution of the i-th designparameter within the subset to the mean calculated threshold voltageadder, and wherein σ_(Vt) ² is the variance (which is the square of thestandard deviation) of the threshold voltage of the transistor on whichthe calculated threshold voltage adder is calculated, σ_(Vt) _(—) ₀ ² isthe variance of the threshold voltage of a nominal device, Δ(σ_(Vt) _(—)_(i) ²) is a change in the variance of the threshold voltage of thenominal device that is scaled to the size of the transistor due to thei-th design parameter within the subset. Each of the Δ(σ_(Vt) _(—) _(i)²) may be positive or negative, i.e., the effect of the i-th designparameter may be to reduce or to increase the variance of the transistoron which the effect of the i-th design parameter is calculated. Thedesign parameters include inherent and external design parameters of thetransistor.

Further, the calculation of the calculated threshold voltage adder maybe repeated to include all semiconductor devices within a subset of asemiconductor chip design that includes a functional semiconductordevice. The subset of the semiconductor chip design includes at leastone functional semiconductor device. In general, the subset of thesemiconductor chip design may include only one functional semiconductordevice, or a “cell,” an array of functional semiconductor devices withinthe semiconductor chip design, a functional block containing a pluralityof semiconductor devices of different types, or the entirety of thesemiconductor chip.

The calculation of the calculated threshold voltage adder may berepeated for each subset of the semiconductor chip design to encompassthe entirety of the semiconductor chip design.

Statistical data is extracted from the calculated threshold voltageadders for the subset of the semiconductor chip design. Depending on thenature of the subset of the semiconductor chip design, the statisticaldata on the calculated threshold voltage adders may be for each devicetype, for each region of the semiconductor chip design, for eachfunctional block, and/or for the entirety of the semiconductor chipdesign.

Parametric yield estimation means is then employed to estimate aparametric yield estimation value for each subset of the semiconductorchip design. The estimation of the parametric yield estimation value maybe based directly on the statistical data on the calculated thresholdvoltage adders for each subset of the semiconductor chip design.Alternately, intermediate quantities may be calculated from the data seton the calculated threshold voltage adders to generate a moresophisticated and accurate estimation of the parametric yield estimationvalue.

Parametric yield estimation means may be a computer program thatcompares overall threshold voltage distribution with a projectedparametric yield value. The parametric yield estimation means includes ayield model that projects or estimates parametric yield of a subset of asemiconductor chip design based on statistical data extracted from thecalculated threshold voltage adders or based on the data set of thecalculated threshold voltage adders of the subset of the semiconductorchip design. The projected value, or the estimated value, of theparametric yield is the projected parametric yield value for the subsetof the semiconductor chip design. Thus, the projected parametric yieldvalue may be for each device type, for each region of the semiconductorchip design, for each functional block, and/or for the entirety of thesemiconductor chip design.

In case the projected parametric yield value is calculated by employingthe full data set of the calculated threshold voltage adders, currentbased performance deviation measurement quantities may be derived.Current based performance deviation measurement quantities may includean average on-current adder and/or an average off-current adder for thesubset of the semiconductor chip design. An average on-current adderand/or an average off-current adder may be calculated for a subset of asemiconductor chip design. The average on-current adder and/or theaverage off-current adder may be positive or negative. The subset maycomprise a device such as a transistor. In case the subset comprises aplurality of devices, calculation of an average on-current adder and/oran average off-current adder may be repeated for every device in thesubset. The average on-current adder and/or the average off-currentadder of the subset in this case is a mathematical average, which couldbe a mean, a median, or a mode, of the set of average on-current addersand/or the set of average off-current adders of the entirety of thesubset of the semiconductor chip design.

Mathematically,

$\begin{matrix}{{{\Delta \; I\; \_ \; {on}^{\; {ave}}} = {\sum\limits_{i = 1}^{n}\; {{\Delta I}\; \_ \; {on}_{i}^{ave}}}},{and}} & \left( {{Equation}\mspace{14mu} 3} \right) \\{{{\Delta \; I\; \_ \; {off}^{\mspace{11mu} {ave}}} = {\sum\limits_{i = 1}^{n}\; {{\Delta I\_}\; {off}_{i}^{ave}}}},} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

wherein ΔI_on^(ave) is the average on-current adder of a device, i.e.,the transistor on which the on-current adder as a distribution iscalculated, n is the total number of the design parameters that arerelated to the threshold voltage adder of the transistor, and ΔI_on_(i)^(ave) is a contribution of the i-th design parameter within the subsetto the average on-current adder, and wherein ΔI_off^(ave) is the averageoff-current adder of the transistor, and ΔI_off_(i) ^(ave) is acontribution of the i-th design parameter within the subset to theaverage off-current adder. As noted above, the average may be a mean, amedian, or a mode. The design parameters include inherent and externaldesign parameters of the transistor.

Calculation of the average on-current adder for the subset and theaverage off-current adder for the subset employs average on-currentadder calculation means and average off-current calculation means,respectively. On-current adder calculation means and/or off-currentadder calculation means may be a stand-alone program that is dedicatedto calculation of the average on-current adder and the averageoff-current adder, and may reside in a computer. Alternately, theon-current adder calculation means and/or the off-current addercalculation means may be integrated into a system, which may includeother automated programs, for designing a semiconductor chip or fordiagnosing parametric yield of semiconductor chips.

The average on-current adder is an average deviation of on-current ofthe subset from a scaling-estimated on-current, which is obtained byscaling of at least one nominal device, due to the design parameters ofthe subset other than inherent geometric dimensions and inherentcharacteristics of at least one device of the subset. The averageoff-current adder is an average deviation of off-current of the subsetfrom a scaling-estimated off-current, which is obtained by scaling of atleast one nominal device, due to the design parameters of the subsetother than inherent geometric dimensions and inherent characteristics ofat least one device of the subset.

The parametric yield estimation value is based on at least one of theaverage on-current adder of the subset and the average off-current adderof the subset. The average on-current adder may be calculated for eachdevice type, for each region of the semiconductor chip design, for eachfunctional block, and/or for the entirety of the semiconductor chipdesign Likewise, the average off-current adder may be calculated foreach device type, for each region of the semiconductor chip design, foreach functional block, and/or for the entirety of the semiconductor chipdesign.

In addition, current based performance deviation measurement quantitiesmay include an average on-current adder and/or an average off-currentadder for the subset of the semiconductor chip design. An incrementalon-current deviation and/or an incremental off-current deviation may becalculated for a device for a subset of a semiconductor chip design. Theincremental on-current deviation and/or the incremental off-currentdeviation may be positive or negative. The subset may comprise a devicesuch as a transistor. In case the subset comprises a plurality ofdevices, calculation of an incremental on-current deviation and/or anincremental off-current deviation may be repeated for every device inthe subset.

Mathematically,

$\begin{matrix}{{{\Delta \; \sigma_{I\; \_ \; {on}}} = {\left\lbrack {\sigma_{I\; \_ \; {on}}^{2} - \sigma_{I\; \_ \; {on}\; \_ 0}^{2}} \right\rbrack^{1/2} = \left\lbrack {\sum\limits_{i = 1}^{n}\; {\Delta \left( \sigma_{I\; {\_ {on}}\_ \; i}^{2} \right)}} \right\rbrack^{1/2}}},{{{{if}\mspace{14mu} \sigma_{I\; \_ \; {on}}^{2}} - \sigma_{I\; {\_ {on}}\; \_ 0}^{2}} > 0},{or}} & \left( {{Equation}\mspace{14mu} 5a} \right) \\{{{\Delta\sigma}_{I\; \_ \; {on}} = {{- {{\sigma_{I\; \_ \; {on}}^{2} - \sigma_{I\; {\_ {on}}\_ 0}^{2}}}^{1/2}} = {- {{\sum\limits_{i = 1}^{n}\; {\Delta \left( \sigma_{I\; {\_ {on}}\_ \; i}^{2} \right)}}}^{1/2}}}},{{{{if}\mspace{14mu} \sigma_{I\; \_ \; {on}}^{2}} - \sigma_{I\; {\_ {on}}\_ 0}^{2}} < 0},} & \left( {{Equation}\mspace{14mu} 5b} \right)\end{matrix}$

wherein Δσ_(I) _(—) _(on) ² is the incremental on-current deviation of adevice, i.e., the transistor on which the on-current as a distributionis calculated, σ_(I) _(—) _(on) ² is the variance of the on-current ofthe transistor, n is the total number of the design parameters that arerelated to the threshold voltage adder of the transistor, σ_(I) _(—)_(on) _(—) ₀ ² is a scaled variance of the on-current a nominaltransistor that is scaled to match the size of the transistor on whichthe on-current distribution is calculated, and wherein Δ(Δσ_(I) _(—)_(on) _(—) _(i) ²) is a contribution of the i-th design parameter to thechange of the variance of the on-current of the transistor. Since σ_(I)_(—) _(on) ²−σ_(I) _(—) _(on) _(—) ₀ ² may be positive or negative, thechange in the on-current deviation may be positive or negative. In otherwords, the incremental on-current deviation, which measures changes inthe standard deviation due to the collective set of the designparameters of the transistor, may be an increment or decrement. Thedesign parameters include inherent and external design parameters of thetransistor.

Likewise,

$\begin{matrix}{{{\Delta\sigma}_{I\; \_ \; {off}} = {\left\lbrack {\sigma_{I\; \_ \; {off}}^{2} - \sigma_{I\; \_ \; {off}\; \_ 0}^{2}} \right\rbrack^{1/2} = \left\lbrack {\sum\limits_{i = 1}^{n}\; {\Delta \left( \sigma_{I\; \_ \; {{off}\_}\; i}^{2} \right)}} \right\rbrack^{1/2}}},{{{{if}\mspace{14mu} \sigma_{I\; \_ \; {off}}^{2}} - \sigma_{I\; {\_ {off}}\_ 0}^{2}} > 0},{or}} & \left( {{Equation}\mspace{14mu} 6a} \right) \\{{{\Delta\sigma}_{I\; \_ \; {off}} = {{- {{\sigma_{I\; \_ \; {off}}^{2} - \sigma_{I\; {\_ {off}}\_ 0}^{2}}}^{1/2}} = {- {{\sum\limits_{i = 1}^{n}\; {\Delta \left( \sigma_{I\; {\_ {off}}\_ \; i}^{2} \right)}}}^{1/2}}}},{{{{if}\mspace{14mu} \sigma_{I\; \_ \; {off}}^{2}} - \sigma_{I\; {\_ {off}}\_ 0}^{2}} < 0},} & \left( {{Equation}\mspace{14mu} 6b} \right)\end{matrix}$

wherein Δσ_(I) _(—) _(off) is the incremental off-current deviation of adevice, i.e., the transistor on which the on-current as a distributionis calculated, σ_(I) _(—) _(off) ² is the variance of the off-current ofthe transistor, n is the total number of the design parameters that arerelated to the threshold voltage adder of the transistor, σ_(I) _(—)_(off) _(—) ₀ ² is a scaled variance of the off-current a nominaltransistor that is scaled to match the size of the transistor on whichthe off-current distribution is calculated, and wherein Δ(σ_(I) _(—)_(off) _(—) _(i) ²) is a contribution of the i-th design parameter tothe change of the variance of the off-current of the transistor. Sinceσ_(I) _(—) _(off)−σ_(I) _(—) _(off) _(—) ₀ ² may be positive ornegative, the change in the off-current deviation may be positive ornegative. In other words, the incremental off-current deviation, whichmeasures changes in the standard deviation due to the collective set ofthe design parameters of the transistor, may be an increment ordecrement. The design parameters include inherent and external designparameters of the transistor.

Calculation of the incremental on-current deviation for the subset andthe incremental off-current deviation for the subset employs incrementalon-current deviation calculation means and incremental off-currentdeviation calculation means, respectively. Incremental on-currentdeviation calculation means and/or incremental off-current deviationcalculation means may be a stand-alone program that is dedicated tocalculation of the incremental on-current deviation and the incrementaloff-current deviation, and may reside in a computer. Alternately, theincremental on-current deviation calculation means and/or theincremental off-current deviation calculation means may be integratedinto a system, which may include other automated programs, for designinga semiconductor chip or for diagnosing parametric yield of semiconductorchips.

The incremental on-current deviation is an increment in statisticaldeviation of on-current of the subset of the semiconductor chip designfrom a scaling-estimated statistical deviation of on-current due to thedesign parameters of the subset other than inherent geometric dimensionsand inherent characteristics of at least one device of the subset. Thescaling-estimated statistical deviation of on-current is obtained byscaling of statistical deviation of on-current of at least one nominaldevice. The incremental off-current deviation is an increment instatistical deviation of off-current of the subset of the semiconductorchip design from a scaling-estimated statistical deviation ofoff-current due to the design parameters of the subset other thaninherent geometric dimensions and inherent characteristics of devices inthe subset. The scaling-estimated statistical deviation of off-currentis also obtained by scaling of statistical deviation of off-current ofat least one nominal device.

The parametric yield estimation value is based on at least one of theincremental on-current deviation of the subset and the incrementaloff-current deviation of the subset. The incremental on-currentdeviation may be calculated for each device type, for each region of thesemiconductor chip design, for each functional block, and/or for theentirety of the semiconductor chip design. Likewise, the incrementaloff-current deviation may be calculated for each device type, for eachregion of the semiconductor chip design, for each functional block,and/or for the entirety of the semiconductor chip design.

Further, on-current distribution calculation means may be employed tocombine a first data set for the average on-current adder of the subsetand a second data set for the incremental on-current deviation of thesubset, and to calculate statistical distribution of on-current withinthe subset. Likewise, off-current distribution calculation means may beemployed to combine a third data set for the average off-current adderof the subset and a fourth data set for the incremental off-currentdeviation of the subset, and to calculate statistical distribution ofon-current within the subset. Each of the statistical distribution ofon-current within the subset and the statistical distribution ofoff-current of the subset contains data for at least two devices withinthe subset. Calculation of the statistical distribution of on-currentand/or the statistical distribution of off-current of the subset may beperformed device by device for each device in the subset, oralternatively, may be performed by grouping each of the first throughfourth data set into sub-groups containing data for at least two deviceswithin each.

The on-current distribution calculation means and/or the off-currentdistribution calculation means may be a stand-alone program that isdedicated to calculation of the statistical distribution of on-currentwithin the subset and the statistical distribution of off-current withinthe subset, and may reside in a computer. Alternately, the on-currentdistribution calculation means and/or the off-current distributioncalculation means may be integrated into a system, which may includeother automated programs, for designing a semiconductor chip or fordiagnosing parametric yield of semiconductor chips.

The statistical distribution of on-current is statistical distributionof on-current of the entirety of devices in the subset. The statisticaldistribution of off-current is statistical distribution of off-currentof the entirety of devices in the subset. A plurality of subsets thatcollectively comprise the entirety of the semiconductor chip design maybe employed to generate a first set of statistical distribution ofon-current of subsets of the semiconductor chip design and a second setof statistical distribution of off-current of the subsets of thesemiconductor chip design. The plurality of subsets may be selected suchthat each of the plurality of subsets is disjoined from one another andhas a unit area and the plurality of subsets collectively constitute theentirety of the semiconductor chip design. In this case, the first setof statistical distribution of on-current of subsets of thesemiconductor chip design is an areal on-current density and a secondset of statistical distribution of off-current of the subsets of thesemiconductor chip is an areal off-current density. Statisticalquantities such as a mathematical average, deviations, variousquantiles, maximum, and minimum may be derived from each of thestatistical distribution of on-current of the subset and the statisticaldistribution of off-current of the subset.

In this case, the parametric yield estimation value is based on at leastone of the statistical distribution of on-current of the subset and thestatistical distribution of off-current of the subset. The statisticaldistribution of on-current of the subset may be calculated for eachdevice type, for each region of the semiconductor chip design, for eachfunctional block, and/or for the entirety of the semiconductor chipdesign Likewise, the statistical distribution of off-current of thesubset may be calculated for each device type, for each region of thesemiconductor chip design, for each functional block, and/or for theentirety of the semiconductor chip design.

Yet further, on-state temperature distribution calculation means may beemployed to calculate on-state temperature distribution of asemiconductor chip that is manufactured with the semiconductor chipdesign. Likewise, off-state temperature distribution calculation meansmay be employed to calculate off-state temperature distribution of asemiconductor chip that is manufactured with the semiconductor chipdesign. The calculated on-state temperature distribution may be directlybased on the areal on-current density, which is the first set ofstatistical distribution of on-current of subsets of the semiconductorchip design described above. The calculated off-state temperaturedistribution may be directly based on the areal off-current density,which is the second set of statistical distribution of off-current ofsubsets of the semiconductor chip design described above. Alternately,the on-state temperature distribution of the semiconductor chip and/orthe off-state temperature distribution of the semiconductor chip may bean ab initio calculation based on calculated threshold voltage adder, anaverage on-current adder, and/or an average off-current adder for eachdevice in the semiconductor chip design.

The on-state temperature distribution calculation means and/or theoff-state temperature distribution calculation means may be astand-alone program that is dedicated to calculation of the on-statetemperature distribution within the subset and the off-state temperaturedistribution within the subset, and may reside in a computer.Alternately, the on-state temperature distribution calculation meansand/or the off-state temperature distribution calculation means may beintegrated into a system, which may include other automated programs,for designing a semiconductor chip or for diagnosing parametric yield ofsemiconductor chips.

The calculation of the on-state temperature distribution of thesemiconductor chip design and/or the on-state temperature distributionmay be performed on a subset of a semiconductor chip design that is lessthan the entirety of the semiconductor chip design, or may be performedon the entirety of the subset of the semiconductor chip design, i.e.,the subset is equal to the entirety of the semiconductor chip design. Incase the calculation is performed on the entirety of the semiconductorchip design, a plurality of subsets that collectively comprise theentirety of the semiconductor chip design may be employed to calculatethe on-state temperature distribution of the semiconductor chip designand/or the on-state temperature distribution of the semiconductor chipdesign. The plurality of subsets may be selected such that each of theplurality of subsets is disjoined from one another and has a unit areaand the plurality of subsets collectively constitute the entirety of thesemiconductor chip design. The on-state temperature distribution of thesemiconductor chip design and the off-state temperature distribution ofthe semiconductor chip design may be nominal temperature distributions,i.e., average temperature distributions. In other words, the on-statetemperature distribution is a statistical average of an ensemble ofon-state temperature distributions. The statistical average may be astatistical mean, statistical median, or statistical mode.

Statistical variations in the on-state temperature distribution and/orin the off-state temperature distribution may also be generated byemploying statistical quantities of the statistical distribution ofon-current of the subsets and/or the statistical quantities of thestatistical distribution of the off-current of the subsets. Thestatistical quantities may include deviations, various quantiles,maximum, and minimum of each of the statistical distributions.Statistical quantile temperature distributions may thus be generatedfrom the statistical distribution of on-current of the subsets and/orthe statistical quantities of the statistical distribution of theoff-current of the subsets. For example, 0.1% quantile on-temperaturedistribution represents the on-temperature distribution that only 0.1%of an ensemble of measured temperature distribution generated from arandomly selected manufactured semiconductor chips is expected to exceedin temperature.

In this case, the parametric yield estimation value may be based on thestatistical average of, and/or statistical variations in, the on-statetemperature distribution and/or the off-state temperature distribution.The parametric yield estimation value may be calculated for each devicetype, for each region of the semiconductor chip design, for eachfunctional block, and/or for the entirety of the semiconductor chipdesign.

Referring to FIG. 5, an exemplary method for designing a semiconductorchip according an aspect of the present invention is shown in a flowchart 500. Referring to step 510, functional requirements of a chip aredefined as in step 210 in the flow chart 200 in FIG. 2. Referring tostep 520, an electronic system level (ESL) description is generatedbased on the functional requirements of the chip as in step 220 in theflow chart 200. Referring to step 530, a register transfer level (RTL)description is generated from the electronic system level (ESL)description in the next chip design phase as in the step 230 in the flowchart 200. Referring to step 540, logic synthesis is performed toconvert the RTL description in the form of the hardware descriptionlanguage (HDL) into a gate level description of the chip by a logicsynthesis tool as in the step 240 in the flow chart 200.

Referring to step 545, parametric value estimation means described aboveis employed to estimate a parametric yield estimation value for each ofat least one subset of the semiconductor chip design in the form of thehardware description language. The parametric yield estimation value maybe calculated for each device type, for each region of the semiconductorchip design, for each functional block, and/or for the entirety of thesemiconductor chip design. Each of the parametric yield estimationvalue, which is referred to as “estimated PY” in the flow chart 500, iscompared with a corresponding parametric yield target value for theparametric yield of the corresponding subset. If any one of theparametric yield estimation value(s) is/are less than the correspondingparametric yield target value for the parametric yield of thecorresponding subset, logic synthesis of the step 540 is re-done for thesubset to increase the parametric yield estimation value by improvingthe semiconductor chip design in the form of the hardware descriptionlanguage. This process may be repeated until each of the at least onesubset of the semiconductor chip design generates parametric yieldestimation value exceeds the corresponding parametric yield targetvalue.

If all of the parametric yield value(s) exceed(s) the correspondingparametric yield target in the step 545, placement and routing toolsutilize the results of the logic synthesis to create a physical layoutfor the chip in the step 550 as in the step 250 in the flow chart 200.

Referring to step 555, parametric value estimation means described aboveis employed to estimate a parametric yield estimation value for each ofat least one subset of the semiconductor chip design in the form of thephysical layout. The parametric yield estimation value may be calculatedfor each device type, for each region of the semiconductor chip design,for each functional block, and/or for the entirety of the semiconductorchip design. Each of the parametric yield estimation value, which isreferred to as “estimated PY” in the flow chart 500, is compared with acorresponding parametric yield target value for the parametric yield ofthe corresponding subset. If any one of the parametric yield estimationvalue(s) is/are less than the corresponding parametric yield targetvalue for the parametric yield of the corresponding subset, placementand routing in the step 550 is re-done for the subset to increase theparametric yield estimation value by improving the semiconductor chipdesign in the form of the physical layout. This process may be repeateduntil each of the at least one subset of the semiconductor chip designgenerates parametric yield estimation value exceeds the correspondingparametric yield target value.

If all of the parametric yield value(s) exceed(s) the correspondingparametric yield target in the step 555, power analysis and timinganalysis is performed in the step 560 as in the step 260 in the flowchart 200. Referring to step 570, the chip design is analyzed to extractdesign specification as in the step 270 in the flow chart 200.

According to the present invention, the semiconductor chip design ischecked for expected parametric yield level of at least one subset ofthe semiconductor chip design by estimating a parametric yieldestimation value for each of the at least one subset. As noted above,the parametric yield estimation value may be calculated for each devicetype, for each region of the semiconductor chip design, for eachfunctional block, and/or for the entirety of the semiconductor chipdesign. The collection of the at least one subset may constitute theentirety of the semiconductor chip design. Since the inventivesemiconductor chip design system can check expected parametric yieldlevel of the semiconductor chip design and provides modification of thesemiconductor chip design, designers may have reasonable confidence thatthe parametric yield of manufactured semiconductor chips according tothe semiconductor chip design would be at an expected level in a designphase of semiconductor chip manufacturing.

Referring to FIG. 6, an exemplary semiconductor chip manufacturingsequence including the steps of chip design according to another aspectof the present invention is shown in a flow chart 600. Referring to step610, a semiconductor chip design is provided as described in steps510-560 of the flow chart 500 in FIG. 5. Referring to step 612, designspecification is generated for the chip as in the step 570 of the flowchart 500 in FIG. 5.

Referring to step 620, data preparation is performed on the chip designto generate various mask levels as in the step 320 of the flow chart 300in FIG. 3. Referring to step 630, semiconductor chips are manufacturedin a semiconductor chip fabrication facility employing varioussemiconductor processing steps including lithography, deposition, andetching. Referring to step 640, the manufactured semiconductor chips aretested and characterized for functionality. Dysfunctional chips aresorted out. Operating frequency, on-state leakage, and off-state leakageare measured on functional chips.

Referring to step 650, parametric yield, i.e., chip limited yield (CLY),is calculated for the group of semiconductor chips that do not sufferfrom random defect yield loss or process limited yield loss based on theresults of the testing and characterization. Assuming a normal scenarioin which the random defect yield loss and the process limited yield lossof the manufacturing process are within expected ranges, delivery ofsufficient number of chips to a customer depends on the parametric yieldloss. If the parametric yield exceeds a minimum parametric yield targetvalue, sufficient number of chips meeting the design specification maybe shipped to a customer, as shown in the step 660.

If the parametric yield is below a minimum target value, analysis on theparametric yield of the semiconductor chip design is performed.Referring to step 670, methods described above may be employed tocalculate a parametric yield estimation value for a subset of thesemiconductor chip design. As noted above, the parametric yieldestimation value may be calculated for each device type, for each regionof the semiconductor chip design, for each functional block, and/or forthe entirety of the semiconductor chip design. Consequently, comparisonof a measured parametric yield value and a corresponding parametricyield estimation value may be performed each device type, for eachregion of the semiconductor chip design, for each functional block,and/or for the entirety of the semiconductor chip design. For any givensubset of the semiconductor chip design, the measured parametric yieldvalue of the semiconductor chip is compared with the correspondingparametric yield estimation value.

The comparison of the measured parametric yield value and thecorresponding parametric yield estimation value may be performedmanually, or preferably, may be performed by parametric yield comparisonmeans, which may be a program dedicated to comparison of the twoparameters, or may be a program incorporated into a test program or acharacterization program.

Referring to step 685, in case the measured parametric yield value andthe corresponding parametric yield estimation value match, which wouldimply that the original semiconductor chip design was designed toachieve the parametric yield of the measured parametric yield value,methods of enhancing parametric yield on future semiconductor chips maybe explored. It is noted that employing a system or methods ofestimating at least one parametric yield estimation value as describeabode according to the present invention can prevent this scenario bymodifying the semiconductor chip design in the design phase. A processmodel is utilized to determine if process parameters, such as adimension or composition of a physical component of a semiconductorchip, may be modified to increase the parametric yield of semiconductorchips in manufacturing or to be manufactured in the future to theminimum target value for the parametric yield. The process model is aset of assumptions or a program based on the set of assumptions forcorrelating process parameters of semiconductor processing stepsemployed during manufacturing of the semiconductor chips with measuredparametric yield value.

Referring to step 690, in case the modification of some processparameters is deemed to be capable of increasing the parametric yield ofsemiconductor chips to be subsequently manufactured above the minimumtarget value of the parametric yield, the process parameters aremodified. The step 60 is repeated to manufacture more semiconductorchips with the modified process parameters. The parametric yield of anew batch of semiconductor chips is expected to be above the minimumtarget value upon execution of a second iteration of the step 640 fortest and characterization of the semiconductor chips and the step 650for comparison of measured parametric yield value and the minimum targetvalue for the parametric yield.

Referring to step 692, in case the modification of process parameters isdeemed incapable of increasing the parametric yield of semiconductorchips to be subsequently manufactured above the minimum target value ofthe parametric yield, at least one design element to modify isidentified and modification to the original semiconductor chip design isperformed. The semiconductor chip design is modified employing the step610 again and subsequent steps described above are repeated. In thiscase, the set of at least one parametric yield estimation value for asubset of the semiconductor chip design may be advantageously employedto identify the at least one design element to be modified. The at leastone design element to be modified may be at least one device type, atleast one region of the semiconductor chip design, and/or at least onefunctional block of the semiconductor chip design to be modified.

In case the measured parametric yield value and the correspondingparametric yield estimation value does not match at the step 670, whichwould imply that the process model is not accurate or there is ananomaly in the parametric yield caused by a yet undetected error in thesemiconductor chip design or in the manufacturing process employed tomanufacture the tested semiconductor chips, the cause of the mismatch isinvestigated. Referring to step 675, it is determined whether themismatch between the measured parametric yield value and thecorresponding parametric yield estimation value may be resolved bymodifications to the process model. Process model fitting means may beemployed to attempt resolving the discrepancy between the parametricmodel estimation value and the measured parametric yield value byaltering process model parameters, i.e., parameters in the processmodel. To effect a resolution of the discrepancy if possible, a measuredprocess parameter database that stores measured process parameter valuesthat are measured during manufacturing of the semiconductor chips may beemployed. The process model fitting means alters the process modelparameters and measures the effectiveness of the process model for eachsetting of the process model parameters as variations in the measuredprocess parameter values are correlated with the measured parametricyield value by the process model. The effectiveness of the process modelmay be measured, for example, by goodness of fit, correlationcoefficients, or by another measure of degree of success in statisticalfitting.

Thus, the process model fitting means is employed to improve accuracy ofthe process model employing the measured process parameter values in themeasured process parameter database. The process model fitting means maybe a dedicated program for fitting, or resolving, the discrepancybetween the parametric yield estimation value and the measuredparametric yield value. Alternatively, the process model fitting meansmay be incorporated in a yield analysis program incorporating otherprograms. In case the measured parametric yield value and thecorresponding parametric yield estimation value may be matched byreasonable and verifiable changes in the process model parameters in theprocess model, the process model is modified with the best-fittingprocess model parameters at step 680. Subsequently, the step 685 isperformed to explore methods of enhancing parametric yield on futuresemiconductor chips. The process flow thereafter is the same asdescribed above.

Referring to step 677, in case the measured parametric yield value andthe corresponding parametric yield estimation value may not be matchedby reasonable and verifiable changes in the process model parameters inthe process model, the likelihood of an anomaly in the parametric yieldcaused by a yet undetected error in the semiconductor chip design or inthe manufacturing process employed to manufacture the testedsemiconductor chips is deemed to be sufficiently high. Consequently,methods to investigate the anomaly in the parametric yield are employedat this point. Once the anomaly is identified, the step 670 may berepeated by comparing a newly estimated parametric yield estimationvalue based on findings on the anomaly with the measured parametricyield value. Alternatively, the step 692 may be performed to identify atleast one design element to modify, and modification to the originalsemiconductor chip design may be performed as described above.

The present invention provides a semiconductor chip manufacturingfacility a system and methods for investigation of the source of thedepressed parametric yield. The inventive system and methods may beemployed upon discovery of depressed parametric yield that does not meeta target, or may be preemptively employed concurrently with or prior toproduction of semiconductor chips. Further, systematic methods areprovided for handling a parametric yield that does not meet a targetvalue.

Referring to FIG. 7, an exemplary sequence for identifying a location ofanomalous functionality of a semiconductor chip according to yet anotheraspect of the present invention is shown in a flow chart 700. Thelocation of anomalous functionality may be the location of the anomalyin the parametric yield at the step 677 described above.

Referring to step 710, a semiconductor chip design is provided asdescribed in steps 510-560 of the flow chart 500 in FIG. 5.

Referring to step 725, on-current distribution calculation means may beemployed to calculate spatial distribution of on-current within thesemiconductor chip. Alternately or in parallel, off-current distributionmeans may be employed to calculate spatial distribution of off-currentwithin the semiconductor chip. The spatial distribution of on-currentand the spatial distribution of off-current within the semiconductorchip are collectively referred to as “current maps” of the semiconductorchip. The spatial distribution of on-current is a map of the density ofon-current in the semiconductor chip. The spatial distribution ofoff-current is a map o the density of off-current in the semiconductorchip. The on-current distribution calculation means and the off-currentdistribution calculation means are as described above.

Current-to-temperature conversion means are employed to convert at leastone of the spatial distribution of on-current and the spatialdistribution of off-current into an estimated spatial temperaturedistribution map, which is herein referred to as a “thermal map.”Current-to-temperature conversion means may be a stand-alone programthat is dedicated to calculation of a temperature distribution map ofthe semiconductor chip, and may reside in a computer. Alternately, thecurrent-to-temperature conversion means may be integrated into a system,which may include other automated programs, for designing asemiconductor chip or for diagnosing parametric yield of semiconductorchips.

Referring to step 730, semiconductor chips are manufactured in asemiconductor chip fabrication facility employing various semiconductorprocessing steps including lithography, deposition, and etching.Referring to step 735, a measured temperature distribution map isgenerated by measuring at least one of manufactured semiconductor chipsin an on-state or in an off-state.

Referring to step 750, the estimated spatial temperature distributionmap and the measured temperature distribution map are compared todetermine whether the two maps match. Referring to step 760, in case thetwo maps match, the semiconductor chip design is deemed to be free ofany apparent design error as determined by the inventive system andmethods.

Referring to step 775, in case the two maps do not match, it isdetermined whether the mismatch between the two maps may be resolved bymodifications to the process model. Process model fitting means may beemployed to attempt resolving the discrepancy between the two maps byaltering process model parameters, i.e., parameters in the process modelas described above. The process model fitting means is the same asdescribed above. The process model fitting means is employed to improveaccuracy of the process model employing the measured process parametervalues in the measured process parameter database. In this case,however, the process model fitting means may be a dedicated programresolving the discrepancy between the estimated spatial temperaturedistribution map and the measured temperature distribution map insteadof resolving a discrepancy between a parametric yield estimation valueand a measured parametric yield value. Alternatively, the process modelfitting means may be incorporated in a characterization program that mayalso incorporate other programs.

In case the two maps may be matched by reasonable and verifiable changesin the process model parameters in the process model, the process modelis modified with the best-fitting process model parameters at step 780.Since the two maps match after modification of the process modelparameters, the semiconductor chip design is deemed to be free of anyapparent design error as determined by the inventive system and methodsas in the step 760.

Referring to step 777, in case the two maps may not be matched byreasonable and verifiable changes in the process model parameters in theprocess model, mismatched spots are identified. It is noted herein thatidentification of the mismatched spots may be a methods to investigatethe anomaly in the parametric yield described above.

Referring to step 792, at least one design element to modify isidentified based on the location of the mismatched spots. Thesemiconductor chip design is modified employing the step 710 again andsubsequent steps described above are repeated. In this case, theidentification of the physical location of the mismatched spots isadvantageously employed to identify the at least one design element tobe modified. The at least one design element to be modified may be atleast one device type, at least one region of the semiconductor chipdesign, and/or at least one functional block of the semiconductor chipdesign to be modified.

Referring to FIG. 8, an exemplary estimated spatial temperaturedistribution map for a semiconductor chip design obtained by theinventive method is shown, in which low temperature regions are shown inblack and high temperature regions are shown in white.

Referring to FIG. 9, an exemplary measured temperature distribution mapfor a semiconductor chip manufactured using the semiconductor chipdesign of FIG. 8 is shown, in which low temperature regions are shown inblack and high temperature regions are shown in white. Anomalousmismatches are found in some areas, which are mismatched spots. One ofthe mismatched spots is labeled with “MS.”

The comparison of an estimated spatial temperature distribution map anda measured temperature distribution map may be performed manually, orpreferably, by an automated system employing temperature distributioncomparison means. The temperature distribution comparison means may be aprogram that receives the estimated spatial temperature distribution mapand the measured temperature distribution map as input data and performsimage processing to produce coordinates of mismatched spots. Theinventive method provides a system and methods for identifying alocation of anomalous functionality to facilitate debugging of asemiconductor chip design.

While the invention has been described in terms of specific embodiments,it is evident in view of the foregoing description that numerousalternatives, modifications and variations will be apparent to thoseskilled in the art. Accordingly, the invention is intended to encompassall such alternatives, modifications and variations which fall withinthe scope and spirit of the invention and the following claims.

1.-16. (canceled)
 17. A method of identifying a location of anomalousfunctionality on a semiconductor chip, said method comprising: by acomputer: determining at least one of spatial distribution of on-currentwithin said semiconductor chip and spatial distribution of off-currentwithin said semiconductor chip; converting one of said spatialdistribution of on-current and said spatial distribution of saidoff-current into an estimated spatial temperature distribution map; andgenerating a measured temperature distribution map of said semiconductorchip in an on-state or an off-state.
 18. The method of claim 17, furthercomprising determining a calculated threshold voltage adder for a devicewithin a subset of a semiconductor chip design including an effect of atleast one design parameter of said subset other than inherent geometricdimensions and inherent characteristics of said device, wherein at leastone of said spatial distribution of on-current and said spatialdistribution of off-current is based on said calculated thresholdvoltage adder.
 19. The method of claim 18, further comprising: storingmeasured process parameter values that are measured during manufacturingof said semiconductor chip; correlating said measured process parametervalues with said measured temperature distribution map with a processmodel; and fitting discrepancy between said measured temperaturedistribution map and at least one of said spatial distribution ofon-current and said spatial distribution of off-current to improveaccuracy of said process model.
 20. The method of claim 18, furthercomprising comparing said estimated spatial temperature distribution mapwith said measured temperature distribution map of said semiconductorchip, wherein a location of discrepancy is identified as said locationof anomalous functionality.
 21. A system for identifying a location ofanomalous functionality on a semiconductor chip, said method comprising:means for determining at least one of spatial distribution of on-currentwithin said semiconductor chip and spatial distribution of off-currentwithin said semiconductor chip; means for converting one of said spatialdistribution of on-current and said spatial distribution of saidoff-current into an estimated spatial temperature distribution map; andmeans for generating a measured temperature distribution map of saidsemiconductor chip in an on-state or an off-state.
 22. The system ofclaim 21, further comprising means for determining a calculatedthreshold voltage adder for a device within a subset of a semiconductorchip design including an effect of at least one design parameter of saidsubset other than inherent geometric dimensions and inherentcharacteristics of said device, wherein at least one of said spatialdistribution of on-current and said spatial distribution of off-currentis based on said calculated threshold voltage adder.
 23. The system ofclaim 22, further comprising: means for storing measured processparameter values that are measured during manufacturing of saidsemiconductor chip; means for correlating said measured processparameter values with said measured temperature distribution map with aprocess model; and means for fitting discrepancy between said measuredtemperature distribution map and at least one of said spatialdistribution of on-current and said spatial distribution of off-currentto improve accuracy of said process model.
 24. The system of claim 22,further comprising means for comparing said estimated spatialtemperature distribution map with said measured temperature distributionmap of said semiconductor chip, wherein a location of discrepancy isidentified as said location of anomalous functionality.